Theory of Perturbation of Electrostatic Field by an Anisotropic Dielectric Sphere

Akhlesh Lakhtakia, Nikolaos L. Tsitsas, Hamad M. Alkhoori

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


The boundary-value problem for the perturbation of an electric potential by a homogeneous anisotropic dielectric sphere in vacuum was formulated. The total potential in the exterior region was expanded in series of radial polynomials and tesseral harmonics, as is standard for the Laplace equation. A bijective transformation of space was carried out to formulate a series representation of the potential in the interior region. Boundary conditions on the spherical surface were enforced to derive a transition matrix that relates the expansion coefficients of the perturbation potential in the exterior region to those of the source potential. Far from the sphere, the perturbation potential decays as the inverse of the distance squared from the center of the sphere, as confirmed numerically when the source potential is due to either a point charge or a point dipole.

Original languageEnglish
Pages (from-to)467-490
Number of pages24
JournalQuarterly Journal of Mechanics and Applied Mathematics
Issue number4
Publication statusPublished - Nov 1 2021

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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